2.1.6.5 ✓ Mathematica. Time used: 0.011 (sec). Leaf size: 11

ode=D[x[t],t]==Cos[t]/Sin[t]; 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \log (\csc (1) \sin (t)) \end{align*}